3x^2-100=500

Solution for 3x^2-100=500 equation:

3x^2-100=500

We move all terms to the left:

3x^2-100-(500)=0

We add all the numbers together, and all the variables

3x^2-600=0

a = 3; b = 0; c = -600;
Δ = b2-4ac
Δ = 02-4·3·(-600)
Δ = 7200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*3}=\frac{0-60\sqrt{2}}{6}
=-\frac{60\sqrt{2}}{6}
=-10\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*3}=\frac{0+60\sqrt{2}}{6}
=\frac{60\sqrt{2}}{6}
=10\sqrt{2}
$